1. Field of the Invention
This invention relates to the field of the electrochemistry, and more particularly, it relates to the coulometric analysis of specific ions in an electrolytic solution.
2. Description of the Prior Art
Coulometric analysis for specific ions in an electrolytic solution is a well known and established technique in the field of electrochemistry. The development of automatic functioning coulometric titrators for carrying out these analyses has produced many devices of which examples may be found in U.S. Pat. Nos. 3,275,533, 3,398,064, 3,441,490, and 3,647,668. Known automatic titration devices in the electrochemical field for conducting coulometric analysis depend upon a feedback loop which supplies an error signal establishing some fixed relationship between the addition of the reactive ion and a reference point at which the titration of the specific ion sought is believed to have been completed. Obviously, the feedback loop principle is a time domain function and suffers from compound errors. The electrodes employed in conducting the electrochemical analysis have an appreciable capacitance characteristic. Also, an appreciable time delay is caused by the diffusion of ions in the cell and principally the reactive ions introduced into the solution by the coulometric flow of current into the cell. Thus, the time delay problems make inaccurate and difficult-to-produce results in the coulometric titration of specific ions in an aqueous solution. The operator or an automatic feature must terminate with high accuracy and precision in electrochemical analysis the introduction of the reactive ion so that the ions may properly diffuse and the cell "coast" to what is believed to be the actual endpoint. The time delay problem varies with ion concentration and kind which also compounds the problem. The actual endpoint also changes not only with different types of ion but with different solvent composition.
It will be apparent that the coulometric titration employs sensors for the detection of the specific ion whose output, according to the Nernst equation, is a voltage proportional to the logarithm of the specific ion concentration. Thus, the most important component of the coulometric titration system is the sensor for the specific ion. The sensor has to indicate when a sufficient amount of the reactive ion has been added to completely convert this specific ion being analyzed for into a product effectively combining the specific and reactive ions into an insoluble or otherwise non-reactive salt. The sensor must be sensitive only to the specific ion being analyzed, and also, the reactive ion must combine only with the specific ion subject to analysis. Further, there must be a definite relationship in the chemical reaction between the specific and reactive ions and freedom from any interferences by extraneous ions with the desired reaction.
Obviously, automatic functioning coulometric titrators usually depend on electrochemical sensors whose voltage output is proportional to the logarithm of the concentration of the specific ion subject to analysis. This relationship is well known as the Nernst equation. This equation is a proper definition for the steady state of a solution or one where the ion concentrations are changing at a very slow rate. Mathematically, the equation defines that a certain percentage change in specific ion concentration will cause an incremental change in sensor output voltage that is the same independent of the actual magnitude of the specific ion concentration. Therefore, in the automatic coulometric titrator, the electrochemical sensor can be incorporated in its function as a percentage change indicator relative to the specific ion concentration.
As will be apparent, the addition of the reactive ion to the test solution at a constant rate produces ambiguities in the sensor's logarithmic voltage output. More particularly, the specific ion sensor changes voltage at the most rapid rate when the specific ion concentration is at equivalence since the largest percent change in specific ion concentration occurs at this point of the analysis. Therefore, the maximum sensor voltage change and the maximum rate of percentage change of specific ion concentration is known as the inflection point of the electrochemical analysis. High accuracy can be obtained with a constant rate of reactive ion addition only if the electrochemical analysis is done at very low rates of reactive ion addition so that the dynamic problems relating to the phenomena do not cause large analysis errors, but the time of analysis is very long.
The above dynamic electrochemical analysis problems can be very severe when the specific ion sensor suffers from capacitive or any energy storage characteristics in the electrolytic solution. The capacitance function in a dynamic electrochemical analysis requires that the specific ions must either enter or leave the region of the sensor for the voltage output to change. In the optimum form of the coulometric titrator, the transfer of the specific ions and voltage output change are usually independent of the specific ion concentration in the solution and dependent only on the physical construction of the sensor. However, where the capacitance function is encountered, these relationships are no longer valid and appreciable time delay errors arise in this electrochemical analysis.
Unfortunately, the capacitive function about the sensor electrode produces a time delay that becomes proportionally larger as the concentration of the specific ions approaches equivalence. At equivalence concentration levels of the specific ions, the time delay problem causes the most error in the electrochemical analysis since the sensor fails to indicate by output voltage the endpoint until some extended period of time after the actual endpoint has been passed by the continued addition of the reactive ion.
The novel coulometric titrator of this invention is arranged to avoid the problems of the time delay error and capacitance function about the sensor electrode. In this coulometric titrator, the new and novel improvement in electrochemical analysis is achieved by scaler (non-time domain) circuitry which reduces the rate of reactive ion addition logarithmically throughout the analysis. In the preferred embodiment of the coulometric titrator, the addition of the reactive ion is made proportional to the ratio of the antilogarithm of the specific ion sensor's voltage output and a certain rate controlling reference voltage. In this coulometric titrator, the factor change in the specific ion concentration remains constant and yields a linear rate of sensor voltage change with time. As a result, any dynamic time delay arising from the characteristics of the sensor in detection specific ion concentration will have a rate controlling influence and not an endpoint controlling influence. The linear rate of change of sensor output voltage with time is set by the rate controlling reference voltage. Thus, the coulometric titrator of the present invention provides not only high speed titrations of great accuracy, but it employs the linear sensor output voltage change to indicate to the operator that the choice of electrochemical analysis parameters is correct.
Since this titrator has been designed to provide reactive ion proportional to the amount of specific ion left to titrate and has no capability for any other reactive ion demand, the stopping point occurs when some unexpected reactive ion demand becomes the predominant user of the available reactive ion. This unexpected reactive ion demand is usually the demand for storage of the reactive ion in solution as free ion. Because the characteristics of ions in solution determine the stopping point, any zero shift in sensor voltage does not change the stopping point, but only changes the rate of speed that the stopping point is approaching. The new and novel design thus permits accurate operation and accurate answers even though the sensor voltage signal has unexpectedly or even intensionally been shifted by some d.c. amount. Other titrators are very dependent on the use of a stable sensor voltage signal and any unexpected shift in sensor voltage signal will cause considerable error in the answer without the operator being conscious of the problem.